CN107092756A - A kind of angular-rate sensor modeling method based on MHD effect - Google Patents
A kind of angular-rate sensor modeling method based on MHD effect Download PDFInfo
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Abstract
The invention discloses a kind of angular-rate sensor modeling method based on MHD effect, comprise the steps of：Step S1, sets up the TRANSFER MODEL of sensor probe；Step S2, sets up the transmission function of primary amplifying transformer；Step S3, sets up the transmission characteristic of rear end instrument amplifying circuit；Step S4, according to the result obtained by step S1, S2 and S3, builds the block mold of sensor.Present system gives sensor probe model, transformer model, the sensor entire process model that rear end amplifying circuit model and three are constituted.This method can quantitative analysis go out under some design parameters, the corresponding Frequency Response of sensor；Also Selection and Design can be optimized to the relevant parameter in sensor, directive function is played in actual development process to sensor by its TRANSFER MODEL.
Description
Technical field
The present invention relates to the in-orbit wideband attitude measurement field of spacecraft, and in particular to one kind is based on MHD effect
Angular-rate sensor modeling method.
Background technology
Camera optical axis measurement accuracy is not enough with bandwidth during camera imaging, will cause image geometry Quality Down, influences
Satellite is without control positioning precision.Platform stance situation of change within the measurable 0~10Hz of traditional measurement sensor, and satellite body and
The structural vibration of its annex, the operating micro-vibration of executing agency all correspond to 0.001Hz~500Hz wideband information.Load diagram
As the thousands of Hz of correspondence data message.Using 2~1000Hz high bandwidth angular-rate sensors, satellite high-precision attitude jitter is carried out
Measurement, can expand payload platform posture and determine bandwidth and improve attitude determination accuracy level.
Current high frequency angular oscillation measuring method has following several：(1) angular oscillation is obtained using the combination of multi-thread vibrating sensor
Information, this method is needed to be calculated indirectly, and number of sensors is more, and the raising of measurement accuracy is limited.(2) optical fibre gyro is utilized
Measurement angle vibration information, this mode precision is high, single expensive, is not suitable for civil applications development.(3) magnetic current bulk effect is utilized
Angular-rate sensor carries out vibration measurement, and such sensor bulk is small, light weight, and precision is high, has wide civil applications to be worth, closely
Ji Nian China has just carried out the art research work, and development time is relatively short.
The content of the invention
It is an object of the invention to provide a kind of angular-rate sensor modeling method based on MHD effect, the party
Method can obtain sensor block mold according to sensor relevant design parameter, be the estimation of sensor amplitude versus frequency characte and sensor ginseng
Number optimized Selection design lays the foundation.
To reach above-mentioned purpose, the invention provides a kind of angular-rate sensor modeling based on MHD effect
Method, is comprised the steps of：
Step S1, sets up the TRANSFER MODEL of sensor probe；
Step S2, sets up the transmission function of primary amplifying transformer；
Step S3, sets up the transmission characteristic of rear end instrument amplifying circuit；
Step S4, according to the result obtained by step S1, S2 and S3, builds the block mold of sensor.
The above-mentioned angular-rate sensor modeling method based on MHD effect, wherein, the step S1 is specific
Comprise the steps of：
Step S11, the electric-field intensity inside conductor fluid is obtained according to Ohm's law：
J=σ (E+V × B) (1)
J is current strength in formula, and E is electric-field intensity, and B is magnetic induction intensity, and σ is electrical conductivity；When under rectangular coordinate system
Magnetic field condition is Bx=0, By=-B0,Bz=0, then it can obtain z-axis directional current intensity：
U in formulaiFor lower plate speed, u is the movement velocity of conductor fluid infinitesimal, and r is O points and lower plate distance；
Step S12, calculates the electromagnetic force for acting on conductor fluid infinitesimal, Fe=JyBz-JzBy=B0Jz；
Step S13, according to Hartmann's constant physical significance, calculating acts on the viscous force of conductor fluid micelle；
I.e.FuFor the viscous force of micelle, M is Hartmann's constant,Wherein h is conductor fluid
Ring thickness, η, ρ, v are respectively the resistivity, density, kinematic viscosity coefficient of conductor fluid；
Step S14, electromagnetic force and viscous force according to suffered by kinematical equation and fluid infinitesimal, obtains conductor fluid micro-
The movement velocity of group：
ρ is the density of conducting liquid in formula；
Step S15, according to the law of electromagnetic induction and the movement velocity of fluid infinitesimal, obtains probe output voltage and angular speed
Transitive relation：
L is electrical conduction current body cavity height, r in formulaRMSFor the root mean square radii of conductor fluid ring.
The above-mentioned angular-rate sensor modeling method based on MHD effect, wherein, in the step S2, structure
The equivalent circuit of transformer is built, according to the transmission function of Kirchhoff's law to transformer：
L in formula1For primary inductance, L2For secondary inductance, L12For primary secondary coil mutual inductance, R1For primary line
The resistance of circle, R2For the resistance of secondary coil, C2For the parasitic capacitance of secondary coil.
The above-mentioned angular speed based on MHD effect passes speed modeling method, wherein, in the step S3,
The transmission characteristic of rear end instrument amplifying circuit is regard as constant value K in the frequency range of sensor responseU。
The above-mentioned angular-rate sensor modeling method based on MHD effect, wherein, will in the step S4
Sensor probe, primary amplifying transformer transmission function corresponding with amplifying circuit with rear end instrument combines, and is sensed
Device entirety TRANSFER MODEL：
In formula：
The advantageous effect of present invention is that：There is provided a kind of angular-rate sensor based on MHD effect
Modeling method, system gives sensor probe model, transformer model, the sensing that rear end amplifying circuit model and three are constituted
Device entire process model.This method can quantitative analysis go out under some design parameters, the corresponding Frequency Response of sensor；Also can be by it
TRANSFER MODEL, Selection and Design is optimized to the relevant parameter in sensor, plays finger in actual development process to sensor
Lead effect.
Brief description of the drawings
Fig. 1 is the flow chart of the angular-rate sensor modeling method of the invention based on MHD effect；
Fig. 2 is conductor fluid flowing equivalent model schematic diagram in sensor probe；
Fig. 3 is the schematic equivalent circuit of transformer.
Embodiment
Below in conjunction with accompanying drawing, by specific embodiment, the invention will be further described, and these embodiments are merely to illustrate
The present invention, is not limiting the scope of the invention.
As shown in figure 1, the invention provides a kind of angular-rate sensor modeling method based on MHD effect,
Comprise the steps of：
Step S1, sets up the TRANSFER MODEL of sensor probe；
Step S2, sets up the transmission function of primary amplifying transformer；
Step S3, sets up the transmission characteristic of rear end instrument amplifying circuit；
Step S4, according to the result obtained by step S1, S2 and S3, builds the block mold of sensor.
The above-mentioned angular-rate sensor modeling method based on MHD effect, wherein, the step S1 is specific
Comprise the steps of：
Step S11, the electric-field intensity inside conductor fluid is obtained according to Ohm's law：
J=σ (E+V × B) (1)
J is current strength in formula, and E is electric-field intensity, and B is magnetic induction intensity, and σ is electrical conductivity；When under rectangular coordinate system
Magnetic field condition is Bx=0, By=-B0,Bz=0, then it can obtain z-axis directional current intensity：
U in formulaiFor lower plate speed, u is the movement velocity of conductor fluid infinitesimal, and r is O points and lower plate distance, such as Fig. 2 institutes
Show；
Step S12, calculates the electromagnetic force for acting on conductor fluid infinitesimal, Fe=JyBz-JzBy=B0Jz；
Step S13, according to Hartmann's constant physical significance, calculating acts on the viscous force of conductor fluid micelle；
I.e.FuFor the viscous force of micelle, M is Hartmann's constant,Wherein h is conductor fluid
Ring thickness, η, ρ, v are respectively the resistivity, density, kinematic viscosity coefficient of conductor fluid；
Step S14, electromagnetic force and viscous force according to suffered by kinematical equation and fluid infinitesimal, obtains conductor fluid micro-
The movement velocity of group：
ρ is the density of conducting liquid in formula；
Step S15, according to the law of electromagnetic induction and the movement velocity of fluid infinitesimal, obtains probe output voltage and angular speed
Transitive relation：
L is electrical conduction current body cavity height, r in formulaRMSFor the root mean square radii of conductor fluid ring.
Therefore the transmission function G of sensor probe1(s) it is
In formula：
B0：Perpendicular to the magnetic field intensity of conductor fluid annulated column, 0.24T is set to；
l：Wire cutting cd length (i.e. the height of ring-shaped chamber), is set to 16.6mm；
rRMS：The root mean square radii of conductor fluid ring, is set to 9.9mm；
h：The thickness of conductor fluid ring, is set to 1.4mm；
ν：Kinematic viscosity coefficientIt is set to 7.5 × 10-8m2/s；
M：The ratio of Harmann number, measurement magnetic force and viscous force, numerical value is set to 10.74.
Transmission function can must be popped one's head in for proportional component K by formula (7)1, differential s and an inertial elementSeries connection
Combination.In addition, magnetic field intensity B0, conductor fluid height l, the root mean square radii r of conductor fluid ringRMS, Harmann number M, electrical conduction current
The kinematic viscosity coefficient ν of body numerical value determines parameter K1, the as height of amplitude-versus-frequency curve；Harmann number M, conductor fluid
Thickness h, the kinematic viscosity coefficient ν of conductor fluid determine the handing-over frequency of amplitude-versus-frequency curve
The numerical value of parameter above is substituted into formula (7), the transmission characteristic that can obtain probe segment is：
Join frequency
The above-mentioned angular-rate sensor modeling method based on MHD effect, wherein, in the step S2, structure
The equivalent circuit of transformer is built, as shown in figure 3, according to the transmission function of Kirchhoff's law to transformer：
L in formula1For primary inductance, L2For secondary inductance, L12For primary secondary coil mutual inductance, R1For primary line
The resistance of circle, R2For the resistance of secondary coil, C2For the parasitic capacitance of secondary coil.
Selection and Design can be optimized to transformer, secondary coil and core material according to transformer model.
The above-mentioned angular speed based on MHD effect passes speed modeling method, wherein, in the step S3,
The transmission characteristic of rear end instrument amplifying circuit is regard as constant value K in the frequency range of sensor responseU.Amplified by adjusting rear end instrument
Circuit gain KU, angular-rate sensor is arranged to proper ratio coefficient.
The above-mentioned angular-rate sensor modeling method based on MHD effect, wherein, will in the step S4
Sensor probe, primary amplifying transformer transmission function corresponding with amplifying circuit with rear end instrument combines, and is sensed
Device entirety TRANSFER MODEL：
In formula：
In summary, present system gives sensor probe model, transformer model, rear end amplifying circuit model and
The sensor entire process model that three is constituted.This method can quantitative analysis go out under some design parameters, the corresponding frequency response of sensor
Characteristic；Also Selection and Design can be optimized to the relevant parameter in sensor by its TRANSFER MODEL, sensor is actually being ground
Directive function is played during system.
Although present disclosure is discussed in detail by above preferred embodiment, but it should be appreciated that above-mentioned
Description is not considered as limitation of the present invention.After those skilled in the art have read the above, for the present invention's
A variety of modifications and substitutions all will be apparent.Therefore, protection scope of the present invention should be limited to the appended claims.
Claims (5)
1. a kind of angular-rate sensor modeling method based on MHD effect, it is characterised in that comprise the steps of：
Step S1, sets up the TRANSFER MODEL of sensor probe；
Step S2, sets up the transmission function of primary amplifying transformer；
Step S3, sets up the transmission characteristic of rear end instrument amplifying circuit；
Step S4, according to the result obtained by step S1, S2 and S3, builds the block mold of sensor.
2. the angular-rate sensor modeling method as claimed in claim 1 based on MHD effect, it is characterised in that
The step S1 is specifically comprised the steps of：
Step S11, the electric-field intensity inside conductor fluid is obtained according to Ohm's law：
J=σ (E+V × B) (1)
J is current strength in formula, and E is electric-field intensity, and B is magnetic induction intensity, and σ is electrical conductivity；Magnetic field under rectangular coordinate system
Condition is Bx=0, By=-B0,Bz=0, then it can obtain z-axis directional current intensity：
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U in formulaiFor lower plate speed, u is the movement velocity of conductor fluid infinitesimal, and r is O points and lower plate distance；
Step S12, calculates the electromagnetic force for acting on conductor fluid infinitesimal, Fe=JyBz-JzBy=B0Jz；
Step S13, according to Hartmann's constant physical significance, calculating acts on the viscous force of conductor fluid micelle；
I.e.FuFor the viscous force of micelle, M is Hartmann's constant,Wherein h is that conductor fluid ring is thick
Degree, η, ρ, v are respectively the resistivity, density, kinematic viscosity coefficient of conductor fluid；
Step S14, electromagnetic force and viscous force according to suffered by kinematical equation and fluid infinitesimal, obtains conductor fluid micelle
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Step S15, according to the law of electromagnetic induction and the movement velocity of fluid infinitesimal, obtains the biography of probe output voltage and angular speed
Pass relation：
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L is electrical conduction current body cavity height, r in formulaRMSFor the root mean square radii of conductor fluid ring.
3. the angular-rate sensor modeling method as claimed in claim 1 based on MHD effect, it is characterised in that
In the step S2, the equivalent circuit of transformer is built, according to the transmission function of Kirchhoff's law to transformer：
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Resistance, R2For the resistance of secondary coil, C2For the parasitic capacitance of secondary coil.
4. the angular speed based on MHD effect passes speed modeling method as claimed in claim 1, it is characterised in that
In the step S3, the transmission characteristic of rear end instrument amplifying circuit is regard as constant value K in the frequency range that sensor is respondedU。
5. the angular-rate sensor modeling method as claimed in claim 1 based on MHD effect, it is characterised in that
In the step S4, by sensor probe, primary amplifying transformer and rear end instrument are integrated with the corresponding transmission function of amplifying circuit
Together, the overall TRANSFER MODEL of sensor is obtained：
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</mrow>
2
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| CN108549787A (en) * | 2018-07-13 | 2018-09-18 | 哈尔滨工业大学 | A kind of rocket large amplitude liquid sloshing method for establishing model based on movement pulsation ball |
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| CN113569375A (en) * | 2021-04-26 | 2021-10-29 | 上海卫星工程研究所 | Non-contact magnetic suspension actuator transfer characteristic modeling and ground calibration method and system |
| CN113822354A (en) * | 2021-09-17 | 2021-12-21 | 合肥工业大学 | Micro-nano probe dynamic characteristic compensation method based on Bayesian inverse calculus modeling |
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| CN109190266A (en) * | 2018-09-10 | 2019-01-11 | 石家庄铁道大学 | A kind of simplified modeling method of the rigid multibody dynamics based on ADAMS software |
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| CN109696181B (en) * | 2018-12-25 | 2020-10-20 | 上海航天控制技术研究所 | Equivalent detection circuit of MHD angular vibration sensor and correction method of frequency band characteristic of equivalent detection circuit |
| CN113569375A (en) * | 2021-04-26 | 2021-10-29 | 上海卫星工程研究所 | Non-contact magnetic suspension actuator transfer characteristic modeling and ground calibration method and system |
| CN113822354A (en) * | 2021-09-17 | 2021-12-21 | 合肥工业大学 | Micro-nano probe dynamic characteristic compensation method based on Bayesian inverse calculus modeling |
| CN113822354B (en) * | 2021-09-17 | 2022-12-06 | 合肥工业大学 | Micro-nano probe dynamic characteristic compensation method based on Bayesian inverse calculus modeling |
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